MathDB

Let

\mathbb{Q}

and

\mathbb{R}

be the set of rational numbers and the set of real numbers, respectively, and let

f : \mathbb{Q} \rightarrow \mathbb{R}

be a function with the following property. For every

h \in \mathbb{Q} , \;x_0 \in \mathbb{R}

, f(x\plus{}h)\minus{}f(x) \rightarrow 0 as

x \in \mathbb{Q}

tends to

x_0

. Does it follow that

f

is bounded on some interval? M. Laczkovich

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